1. Suitable filter

1.1 Definitions

Let the observed message m (t ) = s ₁ (t ) + b ₁ (t ). The signal s ₁ (t ), mixed with noise b ₁ (t ), is assumed to be of known form. An impulse response filterh (t ) is proposed that can detect the presence of signal s ₁ (t ). The filter delivers a signal s ₂ (t ) mixed with a noise b ₂ (t ) (figure 1 ).

The filter sought must maximize...